0
You might consider it an arbitrary definition. However, it is one that makes sense. Look at this sequence:
10 to the power 3 = 1000
10 to the power 2 = 100
10 to the power 1 = 10
10 to the power 0 = ???
10 to the power -1 = ???
10 to thepower -2 = ???
What number would you logically place there? Look at the two sequences - the exponents get reduce by 1 at a time, and the result gets reduced by a factor of 10 every time. If you logically continue this, you get the result that 10 to the power 0 is 1, and you also get reasonable expressions for negative powers.
More formally, certain rules of exponents will continue being valid when powers are defined this way; in this case, mainly, (x to the power a) times (x to the power b) = x to the power (a + b). This continues to be valid ONLY if x to the power zero is defined as 1.
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What is the value of any nonzero base raised to the zero power?
The value of any nonzero number raised to the zero power will equal positive one (1).
What is 1.1 in scientific notation?
1.1 x 10^0 (That's ten to the zero power). Any nonzero real number, raised to the zero power equals 1.
What does a number raised to the power of 0 equal?
Any number raised to the power 0 equals 1.
If any nonzero raised to the power of zero is equal to?
It is always 1
Why any number raise to the power 0 is always 1?
== == The fact is - any nonzero number raised to 0 is always 1. the reason is: suppose a is nonzero. Then by the quotient rule of indices, am/an = am - n Taking m = n we come up with am - m = am/am , which is 1 in view of a nonzero.
